{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1359,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import time\n",
    "from PIL import Image\n",
    "from PIL import ImageDraw\n",
    "plt.style.use({'figure.figsize':(10, 10)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q-Table One"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-table One is used to void the obstacles automatically.\n",
    "### Columns:Nearest|Near|Medium|Far\n",
    "##### Columns register the states\n",
    "### Rows:Up|Down|Turn_left_45 degree|Turn_right_45_degree\n",
    "##### Rows register the actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1360,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#constant\n",
    "Epsilon_start=1\n",
    "Epsilon_final=0.01\n",
    "Decay_Rate=0.00001 #The dacaying rate of the Epsilon, the range of the epsilon is 0.01-1, initially it is 1.\n",
    "Action_times=0 #Rigister the totality of the times of selecting actions, including the random selections and selection based on Q_Table\n",
    "Velocity_tripod=0.289*80\n",
    "Up_D=[-40,-20,0,20,40]\n",
    "Left_D=[-60,-80,-100,-120]\n",
    "Right_D=[60,80,100,120]\n",
    "Robot_R=80\n",
    "Beta=0.9\n",
    "Alpha=0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1361,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Nearest(<50cm)||Near(50cm-130cm)||Medium(130cm-210cm)|Far(>210cm)\n",
    "#Safe distance=1cm\n",
    "States=np.array(['L0R0U0','L0R0U1','L0R0U2','L0R0U3',\n",
    "                'L0R1U0','L0R1U1','L0R1U2','L0R1U3',\n",
    "                'L0R2U0','L0R2U1','L0R2U2','L0R2U3',\n",
    "                'L0R3U0','L0R3U1','L0R3U2','L0R3U3',\n",
    "                'L1R0U0','L1R0U1','L1R0U2','L1R0U3',\n",
    "                'L1R1U0','L1R1U1','L1R1U2','L1R1U3',\n",
    "                'L1R2U0','L1R2U1','L1R2U2','L1R2U3',\n",
    "                'L1R3U0','L1R3U1','L1R3U2','L1R3U3',\n",
    "                'L2R0U0','L2R0U1','L2R0U2','L2R0U3',\n",
    "                'L2R1U0','L2R1U1','L2R1U2','L2R1U3',\n",
    "                'L2R2U0','L2R2U1','L2R2U2','L2R2U3',\n",
    "                'L2R3U0','L2R3U1','L2R3U2','L2R3U3',\n",
    "                'L3R0U0','L3R0U1','L3R0U2','L3R0U3',\n",
    "                'L3R1U0','L3R1U1','L3R1U2','L3R1U3',\n",
    "                'L3R2U0','L3R2U1','L3R2U2','L3R2U3',\n",
    "                'L3R3U0','L3R3U1','L3R3U2','L3R3U3'])\n",
    "Actions=np.array(['Up','Down','Left_45D','Right_45D'])\n",
    "Actions_len=len(Actions)\n",
    "States_len=len(States)\n",
    "# print(Actions_len)\n",
    "# print(States_len)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1362,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Up</th>\n",
       "      <th>Down</th>\n",
       "      <th>Left_45D</th>\n",
       "      <th>Right_45D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>L0R0U0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L0R0U1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L0R0U2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L0R0U3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L0R1U0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Up  Down  Left_45D  Right_45D\n",
       "L0R0U0  0.0   0.0       0.0        0.0\n",
       "L0R0U1  0.0   0.0       0.0        0.0\n",
       "L0R0U2  0.0   0.0       0.0        0.0\n",
       "L0R0U3  0.0   0.0       0.0        0.0\n",
       "L0R1U0  0.0   0.0       0.0        0.0"
      ]
     },
     "execution_count": 1362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_Table_Real=np.zeros((States_len,Actions_len))\n",
    "Q_Table_Real=pd.DataFrame(Q_Table_Real,columns=Actions,index=States)\n",
    "Q_Table_Real.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1363,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***********************************************************\n",
      "Succeed to initialize Q-Table!\n",
      "***********************************************************\n",
      "(64, 4)\n",
      "[[ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "def Initial_Q_Table(Actions_len_,States_len_):\n",
    "    Q_Table_=np.zeros((States_len_,Actions_len_))\n",
    "    print('***********************************************************')\n",
    "    print(\"Succeed to initialize Q-Table!\")\n",
    "    print('***********************************************************')\n",
    "    return Q_Table_\n",
    "Q_Table=Initial_Q_Table(Actions_len,States_len)\n",
    "print(Q_Table.shape)\n",
    "print(Q_Table[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1364,
   "metadata": {},
   "outputs": [
    {
     "data": {
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qxBacwVz+Bwts11SDZYpjnrKNXrMFJxEmwNIcxsvYt38iaz/MbAHAlow5ZsY8trkzswUA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\nuy4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2584dd645c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Draw_map1 funcion is used to train the first Q-Table, which allows it to avoid obstacles\n",
    "im = Image.new(\"I\", size=(2000,2000),color=0) #Color means the degree of Gray scale, 255 means white, 0 means black\n",
    "draw = ImageDraw.Draw(im,mode='I') #mode=\"I\" means the made degree of Gray scale\n",
    "#Draw the black frame around the rectangle\n",
    "draw.rectangle((40,40,1960,1960),255,255)  #the last elements means the color of the inner graph and that of the outer frame\n",
    "def Draw_map1():\n",
    "    draw.ellipse((800,900,880,980),150, 150)\n",
    "    draw.rectangle((1500,1000,1600,1100),0, 0) \n",
    "    draw.ellipse((400,700,600,900),0, 0) \n",
    "    draw.rectangle((200,300,500,600),0, 0) \n",
    "    draw.ellipse((1500,500,1800,800),0, 0) \n",
    "    draw.ellipse((1200,1400,1600,1800),0, 0) \n",
    "    draw.rectangle((700,1200,960,1460),0, 0) \n",
    "    draw.ellipse((300,1600,500,1800),0, 0) \n",
    "    draw.rectangle((100,1100,300,1300),0, 0) \n",
    "    draw.ellipse((1100,250,1300,450),0, 0) \n",
    "    draw.polygon((900, 1070,1120, 1000,1150, 1100, 1100,1090,1050, 1200), 0, 0)\n",
    "    draw.pieslice((750, 1700, 950, 1900), 0,180,0,0)\n",
    "    draw.ellipse((900,550,1050,700),0, 0)\n",
    "    draw.ellipse((650,100,850,300),0, 0) \n",
    "    draw.rectangle((1700,130,1900,330),0, 0)\n",
    "    draw.polygon((150, 180, 200, 180, 250, 120, 230, 90, 130, 100), 0, 0)\n",
    "Draw_map1()\n",
    "plt.imshow(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1365,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Function Scan is used to detect the distance between obstacles and robot.\n",
    "#Nearest(<50cm)||Near(50cm-130cm)||Medium(130cm-210cm)|Far(>210cm)\n",
    "#Furthest scanning distance is defined as 290cm\n",
    "def Scan(Current_x,Current_y,Angle):\n",
    "    Dis_level=0\n",
    "    Obs_dis=Robot_R\n",
    "    Obs_line_x=[]\n",
    "    Obs_line_y=[]\n",
    "    Obs_dis_x=Current_x+Obs_dis*np.cos(Angle/180*np.pi)\n",
    "    Obs_dis_y=Current_y+Obs_dis*np.sin(Angle/180*np.pi)\n",
    "    while(im.getpixel((Obs_dis_x,Obs_dis_y)) is not 0 and Obs_dis<250):#getpixiel obtains the degree of Gray Scale\n",
    "        Obs_dis+=5  #Search interval, can be changed\n",
    "        Obs_dis_x=Current_x+Obs_dis*np.sin(Angle/180*np.pi)\n",
    "        Obs_line_x.append(Obs_dis_x)\n",
    "        Obs_dis_y=Current_y+Obs_dis*np.cos(Angle/180*np.pi)\n",
    "        Obs_line_y.append(Obs_dis_y)\n",
    "    if 80<=Obs_dis<130:\n",
    "        dis_level=0 #Nearear\n",
    "    elif 130<=Obs_dis<210:\n",
    "        dis_level=1 #Near\n",
    "    elif 210<=Obs_dis<290:\n",
    "        dis_level=2 #Medium\n",
    "    else:\n",
    "        dis_level=3 #Far\n",
    "#     Obs_line_xy=list(zip(Obs_line_x,Obs_line_y))\n",
    "#     draw.line(Obs_line_xy, width=12)\n",
    "    return dis_level\n",
    "# print(Scan(1133,1408,20))\n",
    "# plt.imshow(im)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1366,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Is_Crash(Current_x_,Current_y_):\n",
    "    Crash_=False\n",
    "    Degree=[-150,-120,-90,-60,-30,0,30,60,90,120,150,180]\n",
    "    Dis=np.arange(0,70,5)\n",
    "    for i in Dis:\n",
    "        for j in Degree:\n",
    "            x_=Current_x_+i*np.cos(j/180*np.pi)\n",
    "            y_=Current_y_+i*np.sin(j/180*np.pi)\n",
    "            if (im.getpixel((x_,y_)))==0:\n",
    "                Crash_=True\n",
    "                break\n",
    "        if Crash_==True:\n",
    "                break\n",
    "    return Crash_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1367,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(569.03451574373935, 1308.4834986202409, 0)\n"
     ]
    }
   ],
   "source": [
    "def Random_start():\n",
    "    Angle_=0\n",
    "    x_,y_=np.random.random(2)*2000\n",
    "    while(Is_Crash(x_,y_)==True):\n",
    "#         print('Boom')\n",
    "        x_,y_=np.random.random(2)*2000\n",
    "    return x_,y_,Angle_\n",
    "print(Random_start())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1368,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "LRU=[] #LRU register to maximum values of up, left, right.\n",
    "def Direction_min_level(Degree,Current_x,Current_y):\n",
    "    Level=[]\n",
    "    for i in Degree:\n",
    "        Level.append(Scan(Current_x,Current_y,i))\n",
    "    return min(Level)\n",
    "# Left_min=Direction_min_level(Left_D,1133,1408)\n",
    "# Right_min=Direction_min_level(Right_D,1133,1408) \n",
    "# Up_min=Direction_min_level(Up_D,1133,1408)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1369,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42\n"
     ]
    }
   ],
   "source": [
    "def Output_state_index(Left_min_,Right_min_,Up_min_):\n",
    "    LRU=[]\n",
    "    LRU.append(Left_min_)\n",
    "    LRU.append(Right_min_)\n",
    "    LRU.append(Up_min_)\n",
    "    return LRU[0]*16+LRU[1]*4+LRU[2]\n",
    "print(Output_state_index(Left_min,Right_min,Up_min))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1370,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Choose_action is used to selection an action during the training process. It is based on the greedy strategy, if the random \n",
    "#chosen float(0-1) is inferior to current epsilon, robot choose random action to explore, if not, choose maximun Q value\n",
    "#action based on Q Table, more precisely based on the action-state range\n",
    "def Choose_action(Q_Table_,Current_state_,Action_times_):\n",
    "    Epsilon=Epsilon_final+(Epsilon_start-Epsilon_final)*np.exp(-1*Decay_Rate*Action_times_)\n",
    "    State_action_=Q_Table[Current_state_,:]\n",
    "    if(np.random.random()<Epsilon or np.all(State_action_==[0])):\n",
    "        Action_next=np.random.randint(Actions_len)\n",
    "    else:\n",
    "        Action_next=np.argmax(State_action_)\n",
    "    return Action_next\n",
    "#print(Choose_action(Q_Table,20,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1371,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Next_state_F(Current_x_,Current_y_,Action_,Robot_angle_):\n",
    "    R=0\n",
    "    Crash_=False\n",
    "    if Action_==0:\n",
    "        Next_x_=Current_x_+Velocity_tripod*np.sin(Robot_angle_/180*np.pi)\n",
    "        Next_y_=Current_y_+Velocity_tripod*np.cos(Robot_angle_/180*np.pi)\n",
    "#         print(Next_x_)\n",
    "#         print(Next_y_)\n",
    "        if Is_Crash(Next_x_, Next_y_)==True:\n",
    "            Crash_=True\n",
    "            R=-500\n",
    "    elif Action_==1:\n",
    "        Next_x_=Current_x_-Velocity_tripod*np.sin(Robot_angle_/180*np.pi)\n",
    "        Next_y_=Current_y_-Velocity_tripod*np.cos(Robot_angle_/180*np.pi)\n",
    "        if Is_Crash(Next_x_, Next_y_)==True:\n",
    "            Crash_=True\n",
    "            R=-500\n",
    "    elif Action_==2:\n",
    "        Robot_angle_=Robot_angle_-45\n",
    "        Next_x_=Current_x_\n",
    "        Next_y_=Current_y_\n",
    "    elif Action_==3:\n",
    "        Robot_angle_=Robot_angle_+45\n",
    "        Next_x_=Current_x_\n",
    "        Next_y_=Current_y_\n",
    "    return Next_x_,Next_y_,R,Robot_angle_,Crash_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1372,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#     Obs_line_xy=list(zip(Obs_line_x,Obs_line_y))\n",
    "#     draw.line(Obs_line_xy, width=12)\n",
    "def Plot_Move(Vec_x_,Vec_y_):\n",
    "    im1=Image.new(\"I\", size=(2000,2000),color=0)\n",
    "    draw1 = ImageDraw.Draw(im1,mode='I')\n",
    "    draw1.rectangle((40,40,1960,1960),255,255)\n",
    "    draw1.ellipse((800,900,880,980),150, 150)\n",
    "    draw1.rectangle((1500,1000,1600,1100),0, 0) \n",
    "    draw1.ellipse((400,700,600,900),0, 0) \n",
    "    draw1.rectangle((200,300,500,600),0, 0) \n",
    "    draw1.ellipse((1500,500,1800,800),0, 0) \n",
    "    draw1.ellipse((1200,1400,1600,1800),0, 0) \n",
    "    draw1.rectangle((700,1200,960,1460),0, 0) \n",
    "    draw1.ellipse((300,1600,500,1800),0, 0) \n",
    "    draw1.rectangle((100,1100,300,1300),0, 0) \n",
    "    draw1.ellipse((1100,250,1300,450),0, 0) \n",
    "    draw1.polygon((900, 1070,1120, 1000,1150, 1100, 1100,1090,1050, 1200), 0, 0)\n",
    "    draw1.pieslice((750, 1700, 950, 1900), 0,180,0,0)\n",
    "    draw1.ellipse((900,550,1050,700),0, 0)\n",
    "    draw1.ellipse((650,100,850,300),0, 0) \n",
    "    draw1.rectangle((1700,130,1900,330),0, 0)\n",
    "    draw1.polygon((150, 180, 200, 180, 250, 120, 230, 90, 130, 100), 0, 0)\n",
    "    Line_=list((zip(Vec_x_,Vec_y_)))\n",
    "    draw1.line(Line_,width=8)\n",
    "    plt.imshow(im1)\n",
    "    plt.show()\n",
    "#     del draw1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1373,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***********************************************************\n",
      "Succeed to initialize Q-Table!\n",
      "***********************************************************\n"
     ]
    }
   ],
   "source": [
    "Q_Table=Initial_Q_Table(Actions_len,States_len)\n",
    "global Epoche\n",
    "Epoche=0\n",
    "global Action_times #Rigister the totality of the times of selecting actions, including the random selections and selection based on Q_Table\n",
    "Action_times=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1374,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "***********************************************************\n",
      "Epoche\n",
      "0\n",
      "Action_times\n",
      "29\n",
      "Epsilon\n",
      "0.999712941625\n"
     ]
    },
    {
     "data": {
      "image/png": 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d5N8nuSPJZ9YfMgAX0VqL/++uR2hxEWeu2WqtfSHJd0/63bB26h1JPnG126iq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\nAB2JLQCAjsQWAEBHYgsAoKP/Hwx07YlnS6OtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25845178a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***********************************************************\n",
      "Epoche\n",
      "20\n",
      "Action_times\n",
      "1134\n",
      "Epsilon\n",
      "0.988836814887\n"
     ]
    },
    {
     "data": {
      "image/png": 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MoDR/rWmLH+JZqjBrH/C+ZeSgdZVjGyyVR72dm319GmBQPU0RkbI1aul1a9wGLdnbftfj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\nAACQEGELAAAgIcIWAABAQoQtAACAhP5/b6xzGBA80U0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x258466dc160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***********************************************************\n",
      "Epoche\n",
      "40\n",
      "Action_times\n",
      "2842\n",
      "Epsilon\n",
      "0.972260248945\n"
     ]
    },
    {
     "data": {
      "image/png": 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8+QpR0Zo7YRy+3vi1qW4hd4StyuV2xWMfZnIMXWsD4tmBo3SxuvdCvfbUa6yN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25845288cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "***********************************************************\n",
      "Epoche\n",
      "60\n",
      "Action_times\n",
      "3925\n",
      "Epsilon\n",
      "0.961895198506\n"
     ]
    },
    {
     "data": {
      "image/png": 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rrHjvakyNoDUtZuA6cu3Fkt1xc697pOtwbexXr2GjdKBHO9h6UJ1cXY1eqloE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\nYd6C1tnH1z5xaYrLE9Vi/N5be381IWi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       "      <th>L0R3U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L0R3U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L0R3U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R0U0</th>\n",
       "      <td>-258.699520</td>\n",
       "      <td>-112.768000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R0U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R0U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R0U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R1U0</th>\n",
       "      <td>-5.497558</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R1U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R1U2</th>\n",
       "      <td>-0.737870</td>\n",
       "      <td>-64.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R1U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R2U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R2U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R2U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R2U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R3U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L1R3U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R0U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2.847202</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R0U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R1U0</th>\n",
       "      <td>-0.099035</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R1U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R1U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R1U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R2U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R2U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R2U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R2U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R3U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R3U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R3U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L2R3U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R0U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R0U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R0U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R0U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R1U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R1U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R1U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R1U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R2U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R2U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R2U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R2U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R3U0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R3U1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R3U2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L3R3U3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>64 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Up        Down  Left_45D  Right_45D\n",
       "L0R0U0 -257.421773  -40.960000       0.0        0.0\n",
       "L0R0U1    0.000000    0.000000       0.0        0.0\n",
       "L0R0U2    0.000000    0.000000       0.0        0.0\n",
       "L0R0U3    0.000000    0.000000       0.0        0.0\n",
       "L0R1U0    0.000000    0.000000       0.0        0.0\n",
       "L0R1U1 -174.737418  -10.390385       0.0        0.0\n",
       "L0R1U2  -30.198989 -158.982400       0.0        0.0\n",
       "L0R1U3    0.000000    0.000000       0.0        0.0\n",
       "L0R2U0  -63.645456 -140.960000       0.0        0.0\n",
       "L0R2U1   -4.398047   -0.027575       0.0        0.0\n",
       "L0R2U2  -10.933259   -1.886822       0.0        0.0\n",
       "L0R2U3    0.000000    0.000000       0.0        0.0\n",
       "L0R3U0    0.000000    0.000000       0.0        0.0\n",
       "L0R3U1    0.000000    0.000000       0.0        0.0\n",
       "L0R3U2    0.000000    0.000000       0.0        0.0\n",
       "L0R3U3    0.000000    0.000000       0.0        0.0\n",
       "L1R0U0 -258.699520 -112.768000       0.0        0.0\n",
       "L1R0U1    0.000000    0.000000       0.0        0.0\n",
       "L1R0U2    0.000000    0.000000       0.0        0.0\n",
       "L1R0U3    0.000000    0.000000       0.0        0.0\n",
       "L1R1U0   -5.497558    0.000000       0.0        0.0\n",
       "L1R1U1    0.000000    0.000000       0.0        0.0\n",
       "L1R1U2   -0.737870  -64.000000       0.0        0.0\n",
       "L1R1U3    0.000000    0.000000       0.0        0.0\n",
       "L1R2U0    0.000000    0.000000       0.0        0.0\n",
       "L1R2U1    0.000000    0.000000       0.0        0.0\n",
       "L1R2U2    0.000000    0.000000       0.0        0.0\n",
       "L1R2U3    0.000000    0.000000       0.0        0.0\n",
       "L1R3U0    0.000000    0.000000       0.0        0.0\n",
       "L1R3U1    0.000000    0.000000       0.0        0.0\n",
       "...            ...         ...       ...        ...\n",
       "L2R0U2    0.000000   -2.847202       0.0        0.0\n",
       "L2R0U3    0.000000    0.000000       0.0        0.0\n",
       "L2R1U0   -0.099035    0.000000       0.0        0.0\n",
       "L2R1U1    0.000000    0.000000       0.0        0.0\n",
       "L2R1U2    0.000000    0.000000       0.0        0.0\n",
       "L2R1U3    0.000000    0.000000       0.0        0.0\n",
       "L2R2U0    0.000000    0.000000       0.0        0.0\n",
       "L2R2U1    0.000000    0.000000       0.0        0.0\n",
       "L2R2U2    0.000000    0.000000       0.0        0.0\n",
       "L2R2U3    0.000000    0.000000       0.0        0.0\n",
       "L2R3U0    0.000000    0.000000       0.0        0.0\n",
       "L2R3U1    0.000000    0.000000       0.0        0.0\n",
       "L2R3U2    0.000000    0.000000       0.0        0.0\n",
       "L2R3U3    0.000000    0.000000       0.0        0.0\n",
       "L3R0U0    0.000000    0.000000       0.0        0.0\n",
       "L3R0U1    0.000000    0.000000       0.0        0.0\n",
       "L3R0U2    0.000000    0.000000       0.0        0.0\n",
       "L3R0U3    0.000000    0.000000       0.0        0.0\n",
       "L3R1U0    0.000000    0.000000       0.0        0.0\n",
       "L3R1U1    0.000000    0.000000       0.0        0.0\n",
       "L3R1U2    0.000000    0.000000       0.0        0.0\n",
       "L3R1U3    0.000000    0.000000       0.0        0.0\n",
       "L3R2U0    0.000000    0.000000       0.0        0.0\n",
       "L3R2U1    0.000000    0.000000       0.0        0.0\n",
       "L3R2U2    0.000000    0.000000       0.0        0.0\n",
       "L3R2U3    0.000000    0.000000       0.0        0.0\n",
       "L3R3U0    0.000000    0.000000       0.0        0.0\n",
       "L3R3U1    0.000000    0.000000       0.0        0.0\n",
       "L3R3U2    0.000000    0.000000       0.0        0.0\n",
       "L3R3U3    0.000000    0.000000       0.0        0.0\n",
       "\n",
       "[64 rows x 4 columns]"
      ]
     },
     "execution_count": 1374,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Run1():\n",
    "    global Epoche\n",
    "    global Action_times\n",
    "    Crash=False\n",
    "    Current_x,Current_y,Current_a=Random_start()\n",
    "    Epoche_false=0\n",
    "    Vec_x=[]\n",
    "    Vec_y=[]\n",
    "    Vec_x.append(Current_x)\n",
    "    Vec_y.append(Current_y)\n",
    "    while Epoche_false<80:\n",
    "        Current_Left_Obs_Lev=Direction_min_level(Left_D,Current_x,Current_y)\n",
    "        Current_Right_Obs_Lev=Direction_min_level(Right_D,Current_x,Current_y)\n",
    "        Current_Up_Obs_Lev=Direction_min_level(Up_D,Current_x,Current_y)\n",
    "        Current_state=Output_state_index(Current_Left_Obs_Lev,Current_Right_Obs_Lev,Current_Up_Obs_Lev)\n",
    "        \n",
    "        Action_next=Choose_action(Q_Table,Current_state,Action_times)\n",
    "        Next_x,Next_y,R,Next_a,Crash=Next_state_F(Current_x,Current_y,Action_next,Current_a)\n",
    "        \n",
    "        if Crash==True:\n",
    "            Q_target=R\n",
    "            if(Epoche%20==0):\n",
    "                print('***********************************************************')\n",
    "                print('Epoche')\n",
    "                print(Epoche)\n",
    "                print(\"Action_times\")\n",
    "                print(Action_times)\n",
    "                print(\"Epsilon\")\n",
    "                print(Epsilon_final+(Epsilon_start-Epsilon_final)*np.exp(-1*Decay_Rate*Action_times))\n",
    "                Plot_Move(Vec_x,Vec_y)\n",
    "                Vec_x=[]\n",
    "                Vec_y=[]\n",
    "            Epoche+=1\n",
    "            Epoche_false+=1\n",
    "            Next_x,Next_y,Next_a=Random_start()\n",
    "        else:\n",
    "            Next_Left_Obs_Lev=Direction_min_level(Left_D,Next_x,Next_y)\n",
    "            Next_Right_Obs_Lev=Direction_min_level(Right_D,Next_x,Next_y)\n",
    "            Next_Up_Obs_Lev=Direction_min_level(Up_D,Next_x,Next_y)\n",
    "            Next_state=Output_state_index(Next_Left_Obs_Lev,Next_Right_Obs_Lev,Next_Up_Obs_Lev)\n",
    "            Q_target=R+Beta*max(Q_Table[Next_state])\n",
    "            \n",
    "        Q_Table[Current_state][Action_next]+=Alpha*(Q_target-Q_Table[Current_state][Action_next])\n",
    "        Current_x=Next_x\n",
    "        Current_y=Next_y\n",
    "        Current_a=Next_a\n",
    "        Vec_x.append(Current_x)\n",
    "        Vec_y.append(Current_y)\n",
    "        Action_times+=1\n",
    "    return Q_Table\n",
    "print()\n",
    "Q_Table_Final=Run1()\n",
    "Q_Table_Final=pd.DataFrame(Q_Table_Final,columns=Actions,index=States)\n",
    "Q_Table_Final\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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